Cubic Equations | Sum of root of cubic equation
[egin{array}{rrr}x+y+z&=&4\x{2}+y{2}+z{2}&=&14\x{3}+y{3}+z{3}&=&34\end{array}]Therearemanydifferentsetsofsolutionstotheabovesystemofequations.Let(S)bethesumofallpossiblevaluesof(x).Whatis(S?)
[egin{array}{rrr} x + y + z &=& 4 \ x{2} + y{2} + z{2} &=& 14 \ x{3} + y{3} + z{3} &=& 34 \ end{array} ]
There are many different sets of solutions to the above system of equations.
Let (S) be the sum of all possible values of (x). What is (S?)
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